My art deco home was built in 1934/35. Many of the walls are original plaster with 1/4 to 1/2 in. deep irregular texture; the walls have large plaster moldings; and the ceilings are designed with both textured plaster and smooth plaster.

The previous owners painted everything.... great colors with expensive paint, but soon after we moved in, the painted plaster surfaces started to peel... and peel... and peel and peel...

What now? I understand that they didn't properly prep, but now, how do I remove the old paint, so that I may do a proper job of it?

Also, what would be the proper way to prep and prime, when I do remove the old paint?

Additionally, they also put dozens of nails into the walls, which caused a number of "pops" when they were removed... (Yes - I was stupid!) How do I replaster and match the oridinal deep texture?

Welcome , first things first.
Are the walls peeling in sheets or small flaking spots?
Do you have a crawlspace or damp basement? This is a big issue with plaster walls, if the house is damp, the walls will peel. Chances are if they used expensive paint, they used a good primer, this is why I am leaning towards moisture issues.
I bet you have a crawlspace with no plastic down and a dirt floor.
I'm feelin lucky today.
Let us know.

This 1935, art deco house is located in south Louisiana where there aren't any basements. The floors are quarter sawn oak over concrete but with a dirt craw space. The crawl space is covered in plastic. Yes, I did say a concrete floor that is about 2.5 feet off the ground... If you go under the house and look up, all ya' see is concrete!

The walls are solid brick -3 bricks thick, with plaster inside and outside. The interior has beautiful plaster work, with ornate ceilings and heavy moldings of plaster.

Paint is peeling in medium and small flakes... mainly small flakes but slowly over time. Outside there are areas where the paint is peeling in larger sheets.

Oh, and the previous owner was apparently an idiot... remember the dozens of nails in the plaster walls... that is actually more like dozens and dozens of nails in the walls.

In addition, while the previous owner did use good paint (yes we had the cans in the garage), the paint seems to have been just painted over the old paint with little prep. For instance, there is a cinderblock wall on the property where he painted over the dirt, mold and even lichen.... This paint falled soon after we moved in. I received confirmation of this little detail from neighbors.

He also painted the based boards with a very, very heavy layer of paint. Of course, the paint on these old wooden baseboards in NOT peeling. He also painted the smooth plaster walls in the bath with a thick paint that is also peeling... in small flakes.

Plus, there were many other problems that I won't go into... which lend credence to the "idiot" theory.

Paint is coming off the molding, walls, and even the ceilings - a 6 inch in diameter but thick chuck of paint dropped a few weeks ago. I know for sure the ceiling lacks any moisture problems...

Now, back to my original question: Do you or anyone have any suggestions on how I remove this paint? Especially from plaster with various types of textures?

I was trying to get a handle on the issue, before you painted over it again. The underlying issue is still moisture. With a home that old, there is a high probability you have no moisture barriers in place. Being in LA this is a significant problem. The brick walls collect moisture from the air , and so does the plaster, even the ceiling. Without getting into any crazy house science explanations, and make your head spin....
I will tell you there is no easy way to do the paint removal with plaster. You need to first check for lead paint. Then start a long and tedious process of scraping.

My advice is to get a professional in there to help you sort out the issues. I wish it where simpler, and I'm sure someone else has their answer. However this is very complex, and needs to be seen up close. Try www.ashi.com get a home inspector to help understand the issues.
Or try www.buildingscience.com to make your head spin some more.
The problem with the good paint, may be that it cannot let vapor through it. It collects at plaster and the painted surface(hope that makes sense), then the trapped moisture makes it peel off.

Sorry about the bad news, it's the design of the house to act the way it does but I think you need to know what you "could" be up against.
Good luck and tell us how you make out...and if we can be of further help.

I had the house tested for lead paint in 16 locations and unbelievibly none showed the presence of lead. It was almost too good to be true!

Yes. We all know that a house built in 1935 lacks moisture barriers, and while I understand the implactions of moisture, I have done a fair amount of work on this house to reduce moisture as much as possible. The house is sited on a hill and is on well drained soil. Moisture in an uninsulated building in the deep South will always be a problem, but it is not my primary problem at this time.

My neighbors have almost identical houses built at the same time, by the same builder, and they have paint on their walls.... So, I know that if I can get a clean surface and then prep, prime, and paint with the proper materials, I too can live in painted home.

So, that still leads me back to my original request for suggestions on removing paint from textured plaster... 'cuz ya' aint gunna scrap it out of those deep pockets and tiny holes...